Introduction

In cassava, most of the fixed carbon is allocated belowground to grow fibrous roots, for nutrient and water uptake, and storage roots with high starch content. We asked how source (photosynthesis) and sink strength relate to each other, and how the allocation of carbon changes over time. We asked if a change in sink or source strength through phenotypic changes in leaf area and root development could increase yield and used a modeling approach to answer our question.

The root system has fundamental functions in plant growth and development, particularly water and nutrients acquisition and transport, and plant-soil anchorage. Thus, it plays a crucial role in plant development and consequently crop yield. In plants with belowground storage organs, like cassava, the temporal storage of sugars and starch has a specialized function and provides a large sink strength that may compete for carbon with other processes. It is, however, very challenging to quantify these tradeoffs at different developmental stages. High-throughput measurements and advanced phenotyping techniques have greatly enhanced the quantification of root architectural traits such that it has become feasible to build accurate models. The root system architecture (RSA) is often described by geometric measures such as root length, angle, number and length of lateral roots, and branching density. The RSA has been studied extensively in model plants and cereal crops, but not in species with storage roots (Villordon et al. 2014; Khan et al. 2016). Investigation of RSA in tuber root crops is still challenging and this is especially so for cassava, which has a very large root system and is typically grown for a relatively long period of 9–12 months. Recently, a new phenotyping technique for field-grown cassava root systems has been developed (Wilhelm et al. 2022) which prompted us to create a functional structural model of cassava with which we could make source-sink relations insightful.

Cassava (Manihot esculenta Crantz) is an important starchy root crop that is grown globally in tropical and subtropical regions. It is one of the main sources of dietary energy for over 700 million people in tropical and subtropical Africa and contributes to food security as it is particularly drought-resistant and yields at the end of the drought season. Cassava is known for yielding comparatively well in marginal agricultural areas (El-Sharkawy 2004). This makes cassava an especially interesting crop species to study and breeders have asked if the tolerance and yields can be increased further. In 2018, Adu et al. revealed that variations across different cassava varieties could be attributed to crucial traits such as root diameter, traits related to root branching density, and leaf area. These traits were identified as significant contributors and have the potential to enhance nutrient and water-use efficiency in field conditions (Adu et al. 2018; Adu 2020). Functional studies of root traits would benefit greatly from a well-parameterized functional structural root model, which, till now, did not exist.

The root phenotype, including the storage roots, is associated with the dynamics of carbon allocation and shoot–root carbon partitioning. Source–sink relationships are highly dynamic processes describing a complex interplay of carbon availability (source) and use (the sinks). Crop growth and yield can be restricted by both source and sink strength (Jonik et al. 2012; Burnett et al. 2016). Significant advancements in cassava improvement have been achieved in the enhancement of aboveground traits—the source strength (Rosenthal and Ort 2012). However, De Souza et al. (2017) suggested that improved photosynthesis will only lead to greater yields if accompanied by greater storage root growth (De Souza et al. 2017). Previous studies have suggested that genotypes that produce less than nine tuberous roots are constrained by limited sink capacity (Cock et al. 1979). Rosenthal and colleagues discovered that while individual tuberous roots possess restricted storage capabilities, this drawback is counteracted by the commencement of extra tuberous roots (Rosenthal and Ort 2012). We addressed this question of source-sink balancing by model sensitivity analysis, varying leaf growth, and storage root number.

Functional-Structural Plant Models (FSPM) are used to explore and understand the triple interactions between (1) morphological and architectural traits, (2) the environment, and (3) source-sink relations. The FSPM explicitly describes the development of the 3D architecture of plants over time as governed by physiological processes which, in turn, depend on environmental factors (Vos et al. 2010). Thus, they provide insight into key processes underlying plant growth, notably the allocation of resources (Postma and Black 2021). Recently benchmarking of root-focused FSPM models showed the ability of several codes to solve challenging scenarios (Schnepf et al. 2023). Among the well-performing models was OpenSimRoot, an FSPM for describing root growth and function and investigating the complexity of the soil–plant interactions (de Dorlodot et al. 2007; Postma et al. 2017). OpenSimRoot is capable of simulating spatiotemporal dynamics of plant growth, including 3D root architecture, nutrient and water acquisition, and carbon processes underlying plant growth, but requires extensive parameterization. The development of an FSPM for cassava enables many future studies on the dynamics of carbon-related processes determining the potential of manipulating source or sink for crop yield enhancement.

We developed a novel OpenSimRoot model of cassava root development for up to 3-month-old plants. This period includes the critical storage root initiation phase and early bulking. The model was parameterized using data of primarily cassava cultivar KU50 grown under field-irrigated conditions, and the available information on root system architecture in the literature. The cassava version of OpenSimRoot, denoted as MeOSR (acronym of Manihot esculenta OpenSimRoot), was employed to (1) simulate the root system architecture of cassava, (2) provide insights into the dynamics of carbon partitioning to all processes underlying the root and shoot development, and (3) study effects of source-sink manipulation on cassava root production during early growth stages.

Materials and methods

To study the carbon allocation and biomass partitioning of cassava concerning the development of leaf area, fine roots, and storage roots (early bulking), we developed a (3D) functional structural plant model of cassava which, from the simulated geometries, estimates carbon allocation and biomass production. The model was parameterized and compared to experimental data. To construct the model, we used OpenSimRoot, an open-source software for simulating root systems in 3D and associated leaf area and supporting stems (see Postma et al. (2017) for full description). Here, we described the modification of OpenSimRoot and the major aspects relevant to this study.

General features of the MeOSR model

OpenSimRoot implements different submodules for modeling plant growth, root system development, carbon fixation and utilization. The model first simulates the plant structure that is the leaf area, root length, and branching. This ‘geometric’ model serves as the basis for simulating plant physiology (Fig. 1). Leaf area was simulated as a simple ODE for which the leaf area expansion rate of unstressed plants is provided from data series and multiplied with a stress factor, where 1 and 0 denoted unstressed and severely stressed plants, respectively. The stress factor is the minimum of several factors related to non-structural carbon, nutrient and water status, as far as these factors are included in the simulation. Similarly the root system architecture is simulated based on root-class specific growth rates, branching frequencies, growth angles and tropisms. These are all parameterized based on data of observed plants, and can be modulated through stress factors. From the geometric model, resource acquisition and demand are computed. The model balances both over the stress functions. For example, low levels of non-structural carbon lead to reduced growth, with greater impact on roots than shoots.

Fig. 1
figure 1

Schematic illustrating the modeling steps. Note that water status is computed based on steady state assumptions inside the time step has immediate affects, in contrast to carbon and nutrients which have storage pools

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For carbon model, the total carbon income is computed from the photosynthesis process based on a radiation use efficiency (RUE) model, following traditional crop modeling approaches which assume that light capture by a canopy follows Beer’s law and that the RUE is constant. The carbon sinks are computed based on the carbon needed for several carbon-related processes: (1) carbon partitioning for organ growth (i.e., leaf area, stems, and root length), (2) carbon costs (i.e., respiration and root exudation), and (3) non-structural carbon pool (i.e., starch and sugars in a shoot). Carbon needed for leaf growth, for example, is the leaf area expansion rate multiplied by the specific leaf area and divided by the carbon-to-dry-mass ratio. Leaf respiration is the relative leaf respiration times the leaf mass. The carbon costs depend on rates of respiration or carbon expenditure on exudates and are summed over organs. The carbon cost for root exudation also includes association between plant and soil organisms including arbuscular mycorrhizal fungi.

The change in the non-structural carbon pool is simply the difference between the source and sink strength. The model tries to allocate carbon to satisfy all sinks, which is generally possible as a low non-structural carbon pool will lead to stress factors which reduced the growth rates and thereby the sink strength. In extreme cases, here not simulated, the non-structural carbon pool might be completely depleted, and the growth rate might be zero, in which case we assumed the plant dies.

OpenSimRoot can simulate water uptake based on a 3D Richard’s equation for unsaturated water flow, a hydraulic network model in the plant, and a Penman–Monteith equation for transpiration. Uptake and transpiration are balanced over the xylem water potentials, and hydraulic conductivities are reduced when these potentials are low. The hydraulic model was recently benchmarked against known and challenging scenarios and more details can be found in Schnepf et al (2023).

Nutrient uptake can be simulated using an advection–diffusion-sorption transport equation for the soil, and a Michealis-Menten kinetics for the root surface. In this study the nutrient module was not used and is thus not further described. Nutrients, water, or carbon limitations may alter carbon allocation as they affect the forementioned stress factors for the different organs differentially. They can also alter the radiation use efficiency. The model is setup as a system of differential and algebraic equations and solved using a predictor-corrected method.

Adaptations to the OpenSimRoot code to accommodate storage root development

OpenSimRoot was developed for plant species that had no storage roots. We adapted the code so that storage roots can be defined as a separate root class which not only can increase in diameter size (secondary growth) as other roots, but also accumulate starch and thus increase in dry mass. The carbon allocation for storage roots was estimated from relative growth rate (in both elongation and increase in diameter) of unstressed plants and the potential increase in volume times a carbon density (mass per volume). We estimated the rate of diameter increase (cm/day) based on Wilhelm et al. (2022) data and applied to secondary growth rate. The shape of storage roots was adjusted with different scaling factors across the length of storage roots. In this version of OpenSimRoot (MeOSR), accumulated starches and sugars were included in the storage root dry mass. Carbon allocation for storage root development was assigned to support both structural growth and starch accumulation. The model code is available for download under an open-source license at https://gitlab.com/Punyasu/cassava-opensimroot.git.

Field experimental data

To parameterize the model, we used data from experiments on the cassava cultivar Kasetsart 50 (KU50, a high-yielding cultivar). The experiments were carried out at Rayong field crop research center, Thailand (12°44′01″N, 101°08′02″E) from December 2017 to February 2018 (the CASSAVASTORE project; for details see https://www.international-bioeconomy.org/cassavastore_eng, the image data is downloadable at https://doi.org/10.5281/zenodo.5883369). The cassava plants were grown from stem cuttings in an irrigated field with loamy-sand soil. Fertilizer application followed general practice suggested by Rayong Field Crops Research Center of the Department of Agriculture (DOA), Thailand. The stem cuttings were planted at equal inter- and intra-row distances of 60 cm. Five individual plants (biological replicates) were harvested every two weeks between the fourth to the twelfth week (28 to 84 Days After Planting, DAP). For each harvesting time point, the number of attached leaves, fallen leaves, stems, fibrous (nodal and basal roots), and storage roots were counted manually. All plant parts were oven-dried at 80 °C until constant weight to determine dry mass. The leaf area of fully expanded leaves was measured using leaf image analysis according to the method of Cock, H. et al. (2014). Briefly, we took a photograph of a fully expanded leaf when it was inserted between two laminae of the leaf area apparatus (LAA) with marked scale by holding a camera vertically above the LAA. The leaf area was then analyzed using ImageJ software by setting a Known Distance according to the marked scale on the photograph. The shape of the root system was characterized by measuring the widest and longest part of the excavated whole-root system as root system girth and length following the procedure of Wilhelm et al. (2022). The environmental data, e.g., precipitation, air temperature, solar radiation, relative humidity (RH), soil moisture, and wind speed were also recorded using a weather station placed at the edge of the experimental field (the CASSAVASTORE project).

Parameterization

Parameters in the MeOSR are based on data from cassava plants taken during the first 3 months after planting. The plant traits were derived as follows. The leaf area expansion rate (LAXR) was calculated by fitting a smooth spline to the leaf area data over time and determining its derivative (cm2 per day). Specific leaf area (SLA, cm2 per gram) was provided as a ratio of leaf area to leaf mass at different time points. The leaf senescence rate was estimated based on the number of fallen leaves times the average area of an individual leaf. Potential rates of dry mass accumulation in leaf, stem, fibrous, and storage roots were calculated using the same procedure as for LAXR but using data for the respective masses. The radiation use efficiency (g C per mol of intercepted photons) was estimated based on the light saturation point of net leaf CO2 uptake of cassava (Pn max) which represented the efficiency of the crop to produce dry mass (in terms of carbon capture), relatively to maximum light intercepted by the canopy. Maximum photosynthesis rates (Pn max) range from 20–30 µmol CO2 per meter of leaf per sec and are typically achieved at light levels of around 1000 µmol PAR per square meter per sec (De Souza and Long 2018; Santanoo et al. 2019; De Souza et al. 2020). This gives a RUE of 0.24—0.36 g C per mol PAR. We used a mid-value of 0.3. The relative respiration rate of leaves (gram C per gram dry mass per day) was approximated based on 13C measurement of intact French bean leaves (C3 plant, Nogués et al. 2004) and very closed to the value for cassava leaves estimated from dark respiration measurements (data unpublished). We also parameterized the maximum amount of carbon allocated for shoot growth based on the ratio of shoot dry mass to total plant dry mass. Maximum carbon allocation for secondary growth was assumed to be 70% based on average starch content in cassava storage roots. Carbon to dry mass ratio is 0.444 in which calculated from amount of carbon in starch molecule as starch is the main components of cassava plant.

The parameters for the root system architecture (e.g., secondary root growth, root system width, angle, and gravitropism) were estimated from excavated cassava root systems and the literature (Kengkanna et al. 2019; Müller-Linow and Wojchiechowski 2022; Wilhelm et al. 2022). The MeOSR model contains two main types of roots: (1) adventitious roots, including nodal roots (emerge from nodes on the stem cutting) and basal roots (emerge only from the base of the stem cutting), and (2) storage roots that grow from the base of the stem cutting but have strong secondary root growth and starch accumulation. The number of storage roots ranged from 6–8 roots (Kengkanna et al. 2019). The maximum numbers of nodal and basal roots were set as 10 and 50 roots, respectively. Root elongation rates for each root type were calculated from rates of root lengthening over time. Secondary growth rates of storage roots were estimated from the increase in radius over time and with distance from the base of the root. Root angle and gravitropism assumed from image analysis of excavated root systems. The logging data from the weather station was transformed to daily averages and applied to the MeOSR model – thus not simulating diurnal rhythms. The used parameter set is provided in the aforementioned git repository and supplementary Table S1.

Comparison of simulation results to experimental data

We compare measured to simulated growth of leaves, stems, and roots and their mass fractions. We used measurements from the same experiments that were used to parameterize the model. We thereby verified that the model gives a coherent representation of the observed plants. In addition, the simulated root systems and their traits were compared to images and image-based quantification of root traits of 3-month-old cassava plants grown under both controlled environments (Kengkanna et al. 2019) and field experiments (Müller-Linow and Wojchiechowski 2022; Wilhelm et al. 2022).

The comparison presented us with a small challenge, as the classification of roots in the model is different from the one used in the experimental data. The classification in the model is static and does not change over time (Fig. 2). Experimentally, storage roots are often classified simply based on diameter. This is a dynamic classification: a root starts as a fibrous root and becomes a storage root once it grows thicker than a given diameter. We implemented this ‘diameter’ based classification in the model, next to its static classification, and compared the results when (1) the type of root was pre-defined from its emergence and (2) defined based on diameter thresholds (5 mm to distinguish fine roots from storage roots). Thus, we asked if the time course of important traits is strongly influenced by the classification system.

Fig. 2
figure 2

Two bases of root type classification. The left panel represents different root types by highlighting them with different colors. In the right panel, a root segment that has a diameter of less than 0.5 cm is in red, while equal to or greater than 0.5 cm is in grey (except stem cutting, which is in blue). The figures show 3D structure of cassava root systems at 30 DAP (top panel) and 84 DAP (lower panel)

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Sensitivity analysis

To answer our original questions, we performed a model sensitivity analysis in which we varied the LAXR and the number of storage roots and determined the effect of these traits on the photosynthesis rates and storage root yield at 84 DAP. Based on the carbon balance model, the higher carbon demand for storage root growth due to its increasing number would increase carbon competition between storage roots and other carbon-related processes including carbon for leaf and stem growth. While the carbon demand from leaves due to the increasing LAXR would expect to compete with carbon other carbon sinks, but potentially also increase future light capture and carbon fixation.

LAXR was perturbed to explore both increased and decreased capacities, with variations of 10% and 50%, as well as shifting LAXR by + 20/-5 days to represent rapid and slow-growing patterns, respectively (Fig. S1). In the + 20-day scenario, the LAXR exhibited an accelerated, 20-day period of advancement compared to the normal, followed by a period of constant growth (the last 20 days) until the end of the simulation. In the -5 Day scenario, the growth rate was delayed by 5 days compared to the normal condition. During the first 5 days, the LAXR matched that of day 0 in the normal condition. Additionally, the sink strength was modified by increasing the number of storage roots (SR) from 7 to 10 and 13.

Statistical analysis

Statistical analysis was performed using R Statistical Software (version 4.2.2) (R Core Team 2013). For parameterization, we fitted smooth splines with a smoothing parameter (spar) in the range 0.5–0.8 to avoid overfitting. For the results, we present the Root-Mean-Square Error (RMSE) to evaluate the simulated data against the experimental data. For the RMSE calculation, we selected the simulation results only on the same days as the experimental data and then calculate RMSE with number of experimental observations (five time points, and at each time point the mean of 5 observations).

Results

MeOSR simulation compared to experimental results

The MeOSR model rendered images of root systems that resembled those of real-life cassava root systems quite well, and several morphological characteristics agreed with the cassava literature (Figs. 3 and S2). The simulated number and length of the storage roots agree with the excavated roots, but the simulated storage roots looked shallower than those of the excavated root systems (Fig. 3). The maximum diameter of the simulated storage roots was thinner than that of excavated roots, probably because the parametrization was based on mean increases in diameter and did not simulate the variation that is present in real-life root systems. The mean length of individual fibrous roots (nodal and basal roots) was shorter in the simulation. Note that the simulated root system is intended to represent the whole root system, whereas the excavated root systems only show the shoveled crowns from which fine and deep roots might have been lost.

Fig. 3
figure 3

Visual comparison of an excavated (A) and simulated (B) cassava root system at 84 days after planting. C The table compares root traits of cassava of real-life and simulated plants at 84 DAP. *) Measurement based on image analysis of the same plants as in Wilhelm et al. (2022). **) The MeOSR variables represent means ± standard deviation of the mean across nine simulations with 6,7, and 8 storage roots and three replications. [1] Connor and Cock (1981) Mean ± standard deviation; [2] Kengkanna et al. (2019) Mean ± standard error; [3] Wilhelm et al. (2022)

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The predicted plant growth and biomass production responsible for the modeled cassava root structure aligned well with the measured data (Fig. 4). The predicted total plant dry mass (TDM) fitted the experimental data very well (Fig. 4A). Shortly after planting, the cassava cuttings grew rapidly new shoots with photosynthetic active leaves (as reported in Alves 2001). This resulted in the relatively high leaf (LMF, Fig. 4B) and stem mass fraction (SMF, Fig. 4C) and consequently low fibrous root mass fraction (fRMF, Fig. 4D), during the first months. This behavior was well-captured by the model. However, during the second and third MAP, LMF (Fig. 4B) was underestimated. The experimental data might have a higher LMF because of an underestimation of root biomass during root excavation of real-world plants and the associated loss of small roots due to the senescence of fibrous roots which is not simulated (Izumi et al. 1999; Gregory and Wojciechowski 2020).

Fig. 4
figure 4

A Simulation of cassava whole plant dry mass (g plant) over time compared to experimental data (dots, n = 5). B Leaf mass fraction (LMF, gram leaves per gram plant). C Stem mass fraction (SMF, gram stems per gram plant). D Fibrous root mass fraction (fRMF, gram roots per gram plant). E Storage root mass fraction (sRMF, gram roots per gram plant). Red and blue lines represent root mass fractions based on simulated root types and diameter root classes (Fibrous roots Φ < 0.5 cm and Storage roots Φ ≥ 0.5 cm), respectively. Blue arrows indicated a stage of storage root initiation, i.e., root diameters larger than 0.5 cm were found (at 56 DAP). The results from a single simulation with 7 storage roots. RMSE = Root Mean Square Error of the prediction versus the measurement, see statistics section. Note that at 70 DAP only one plant sample had storage roots

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At the beginning of plant development, the fibrous root mass fraction (fRMF, Fig. 4D) was relatively low compared to the LMF and SMF. It then quickly increased as more fibrous roots started to grow. We had no measurements during this early period, but the model simulated this expected trend well and had the correct fRMF at 28 DAP. After 28 days, the measured fRMF was declining, as is generally true for older (Henn and Damschen 2021) and larger (Poorter et al. 2012) plants. The model predicted this decline quite well, especially when roots were classified based on diameter, as is done in the experimental data (Fig. 4E, blue line). The diameter classification results in an estimation of the onset of storage root formation at 56 DAP (Fig. 4E, blue arrows). The experimental data estimated this at 70 DAP, at which one out of four plants had storage roots.

Cassava root system development and SR formation

Given that the model represents real-life plants close enough, it may provide insights into various dynamic processes that are difficult to monitor in real-life plants. We visualized the time course of root growth in both width and depth (Fig. 5A). The fibrous roots, including nodal and basal roots, spread in all directions, while the storage roots remained shallow throughout the simulation. This has been a selection criteria as shallow storage roots are easier to harvest. The root system dry mass increased exponentially, whereas the length increased rather linearly (Figs. 5B and C). When comparing the linear increase in total root length with the exponential accumulation of root dry mass, we observed the dynamic changes in specific root length (SRL) (Fig. 5E). SRL exhibited its highest value at 42 DAP and subsequently declined, illustrating the varying SRL throughout different developmental stages of the cassava root system. The decrease in SRL from 42 DAP onwards was primarily attributed to the development of storage roots. One might expect that the average root diameter would show an inverse pattern from SRL, but it was rather constant over time (Fig. 5D). Storage roots do grow thicker and contribute strongly to the total mass of the root system (Fig. S3), but their length is short compared to that of fibrous roots, and thus they do not ‘weigh’ heavily into the average diameter estimation. The decline in SRL suggests that the older plants prioritize carbon allocation to secondary growth over primary growth, and we remark that they do this well before a high root length density has been achieved and before canopy closure (data not shown).

Fig. 5
figure 5

Simulation of cassava root system development (A) Cassava root systems are rendered in 3D with Paraview. B Total root dry mass (g). C Total root length (m). D Average root diameter (mm). E Specific root length (SRL, meter per gram). The error bars represent the standard deviation across simulations with 6, 7, and 8 storage roots, with three replications for each case

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Carbon budgets

In the simulation, carbon can be allocated to organ development (leaves, stems, and roots), respiration (relative to organ size), and carbon for root exudation, or it can be stored as non-structural carbohydrates (NSC; soluble sugars and starch). The model allocates according to the absolute sink strength of all processes and will only reduce growth if the NSC concentrations are low (close to zero). An increase in NSC thus suggests that at that moment, source strength is greater than sink strength, and vice versa. Figure 6 shows the cumulative amount of carbon partitioned to the aforementioned processes as a percentage of the total amount of carbon fixed (including the initial NSC content of the cutting). Young plants used most carbon for growth, whereas during the second month, NSC accumulated (Fig. 6A). NSC was the largest carbon fraction at 44 DAP and declined (relatively) afterwards. As plants grew larger, they spent an increasing proportion of their fixed carbon on plant respiration. At the end of the 84 days, 42% of the fixed carbon was respired.

Fig. 6
figure 6

Cumulative carbon acquisition is partitioned into processes. A percentage of carbon is spent on organ growth, root exudation, respiration, and non-structural carbohydrate (NSC). B percentage of carbon in leaf, stem, and root mass. C percentage of carbon lost by leaf, stem, and root respiration. One-day resolution for a single simulation with 7 storage roots

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Figure 6B zooms in on the partitioning of carbon over the structural biomass. Initially, carbon was mainly invested in shoot growth (i.e., leaves and stems). The proportion of carbon for root growth grew steadily to 36% at 54 DAP (Fig. 6B). The proportion of carbon for secondary root growth continuously increased, in contrast to primary root growth. It was consistent with the emergence of storage roots (diameter larger than 0.5 cm) at 56 DAP (Fig. 4E, blue arrows). We note that just before SR initiation, the NSC was large. We think that a high NSC concentration might induce SR formation in real-life plants, and the simulation is consistent with this hypothesis.

Carbon allocation varies at the different growth stages

Figure 7 shows the finite difference in carbon that was allocated to each carbon-related process daily (g C per day). Carbon allocated to NSC increased every day until 44 DAP (Fig. 7A, yellow region), then kept constant till 70 DAP (Fig. 7A, blue and green regions), and then dropped. Carbon for plant organ growth increased first slowly and then shifted the state to be approximately exponential (Fig. 7A, blue region). Until 31 DAP, the amount of carbon allocated to leaf and stem growth was greater than that allocated to root growth. From 31 to 56 DAP, more carbon was allocated to roots (Fig. 7B, yellow region). After 56 DAP, leaf growth received more carbon. The period of low carbon allocation to shoot growth correlated with a period of high allocation to NSC, indicating low sink strength and possibly in preparation for storage root formation (Fig. 7A, blue region). The yellow and blue regions thus show a period of slow shoot development, accumulation of NSC, and the start of exponential root growth. The green region indicates a period in which a large amount of carbon is allocated to shoot growth which is necessary to increase the leaf area and thereby canopy photosynthesis as the sink strength of the by now formed storage roots is large. We expect this pattern to be temporal, and that when the canopy closes (normally after three months) most carbon will go to the storage roots.

Fig. 7
figure 7

Carbon allocation within a cassava plant. A finite difference of carbon (gram per day) is allocated at that day to each process. B finite difference of carbon (gram per day) allocated for the growth of leaves, stems, and roots. The yellow area highlights the period during which plants allocated more carbon to roots than to shoots, the blue area highlights a transition period, and the green area highlights a strong allocation to shoot growth

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Estimation of source and sink effects on photosynthesis and storage root yield

We asked if a greater allocation to leaf growth might result in larger photosynthesis and thus varied the leaf sink strength, which is a function of the LAXR. However, as the model simulated a large accumulation of NSC, we may also need to increase the sink strength for storage root formation to utilize the photosynthates and ‘convert’ them into ‘yield’. We employed the MeOSR model to examine the effect of source strength perturbation (i.e., leaf area expansion rate, Fig. S1) along with sink capacity modification (i.e., number of storage roots) on storage root production.

Cassava plants with a greater number of SR had a greater storage root dry mass (SRDM) across nearly all leaf area scenarios. On the other hand, the presence of a large leaf area did not necessarily lead to increased SRDM (Fig. 8A). Plants with the same SR number produced comparable SRDM, although they differed in leaf area development. The SRDM did fluctuate with increasing leaf area somewhat, and the greatest SRDM was not achieved with the greatest LA, which shows there is mild competition for carbon allocation in the model when we increase both leaf and SR sink strength. It might show that excessive shoot development can go at the cost of yield. However, although the scenarios with the greatest leaf area might have slightly lower SRDM at 84 DAP, they have the greatest photosynthesis rates and are expected to produce a greater yield in the month to follow. Further investigations, utilizing either computational-based or experimental-based methods and considering longer plant ages, are required to gain deeper insights.

Fig. 8
figure 8

Simulation of storage root dry mass from cassava plants with different source (leaf growth rates) and sink strength (storage root number). Manipulation of leaf area expansion rate affects total leaf area (A) and photosynthetic rate (B) at 84 DAP. Variation in leaf area expansion rate is represented by different symbols. Black circles show leaf area as parameterized based on field data. The leaf area at 0.6 m2 corresponds with LAI 1.7. Graphs show the means ± standard error of the mean across ten replications per scenario. LAXR; Leaf Area Expansion Rate (cm2 per day)

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Discussion

We developed the MeOSR model, a mathematical approach to study the dynamics of growth-related carbon processes and their relation to root system structure during cassava storage root formation (the first three MAP). The cassava growth was simulated based on a non-limited soil water and nutrient condition. The simulated root architectural traits, biomass, and mass fractions were overall in good agreement with the measured data. The model suggests that cassava plants go through several stages of development in which they shift their carbon allocation to different organs and processes. Plant growth was largely sink-limited, resulting in the accumulation of NSC before storage root initiation. Increasing the number of storage roots increased their yield, especially when combined with faster leaf area development.

The cassava root system plays a crucial role in resource acquisition and crop productivity, notably the storage root yield. The balance between resource investment for overall plant growth, storage root development, and other processes is a critical factor in determining cassava yield. However, this balance has received relatively little attention, partly due to the challenges of accessing the dynamics of carbon allocation experimentally. The model effectively simulated cassava growth, including root development and storage root production during the early stage of root bulking. By accurately representing the characteristic 3D structure of the root system, we were able to simulate the root system architecture during the first 3 months of growth, till early bulking. From the geometric model, the simulation estimated the underlying carbon allocation process for cassava root growth and development.

At 84 DAP, the appearance of the 3D simulated root systems was comparable to the excavated root system (Figs. 3A and S2). The root system was, in comparison to other crops, relatively shallow and sparse. This seems to agree with field observation reported in the literature (El-Sharkawy 2004; Gregory and Wojciechowski 2020). The simulated storage roots appeared somewhat shallower than those of excavated root systems, and a small deviation in predicted mass fractions of leaf and root was found at the middle stage of the first phase of vegetative growth (Figs. 4B, D, and E). The deviation in root mass fraction (Figs. 4D and E) may occur due to the MeOSR model predicting the root mass based on the geometry of the root system. The model simulated relatively high elongation rates during the early growth stage, and this is in agreement with reports from Izumi and Iijima (2002) but also led to a relatively high root mass fraction, greater than the one measured in our dataset. Similarly, the leaf area (Fig. S4) was in good agreement with the measurements, but the leaf mass fraction was underestimated. However, the growth prediction in terms of total plant dry mass was in line with experimental data (Fig. 4A). We conclude that the model describes real-life plants well enough to study its other predictions and use it in sensitivity analysis.

The examination of root traits provided us with valuable insights into plant form and function. The root economic spectrum theory suggests that species follow one of two strategies: (1) a “fast” belowground resource acquisition strategy where carbon is invested in long, narrow-diameter roots with minimal biomass investment (high specific root length; SRL), and (2) a “slow, but long-lived” strategy where carbon is invested in thicker-diameter roots with denser tissue and a longer life span (low SRL) (de la Riva et al. 2021). A third strategy was identified as the ‘outsourcing’ strategy, in which species strongly rely on symbioses for their nutrient acquisition, particularly mycorrhizal fungi (Bergmann et al. 2020). In this study, SRL decreased after 28 DAP (Fig. 5E) suggesting a fast establishment phase is followed by a phase of secondary thickening which can increase water and nutrient transport, and notably storage capacity. However, this shift may come at the cost of reduced nutrient and water absorption. Possibly, at this time mycorrhizal colonization starts to contribute strongly to nutrient uptake, and the plant has a lesser need for fine roots. Cassava relies strongly on arbuscular mycorrhizal fungi (AMF) (Ceballos et al. 2013; Séry et al. 2016) and compared to many other crops, the SRL of cassava is low (Adu 2020). While further investigation is required to establish the link between cassava root traits and the root economic spectrum, or AMF association, our model offers a comprehensive quantification of root system traits, which can serve as valuable support for future research endeavors.

The initiation and subsequent growth of tubers is a biochemically and morphologically coordinated change (Amarullah et al. 2017). The simulation revealed a continuous accumulation of NSC (excess carbon harvested from photosynthesis, Figs. 6A and 7A) until it declined during the growth of the SRs. This is consistent with our hypothesis that accumulation of NSC induces SR formation and in agreement with studies of cassava grown in vitro (Wu et al. 2014) and potatoes (Wellensiek 1929; Vreugdenhil and Helder 1992). During the second month, and prior to the formation of storage roots, NSC increases in part because shoot growth, and associated carbon allocation to shoots, slow down (Fig. 7B). Similar slowing down of shoot growth has been reported for potato (Driver and Hawkes 1943; Rasumov 1931). Barros et al. (1978) suggested that cassava leaf growth is inhibited by the strong sink strength of the storage roots. We doubt that a direct competition is taking place, given the accumulation of NSC. More likely, high NSC inhibits shoot growth. Limited sink capacity in cassava can negatively feedback on photosynthesis (De Souza et al. 2017).

Crop improvement has mostly targeted aboveground traits, notably photosynthesis, i.e., source strength. Our results suggest that this will not lead to a greater yield unless the storage root sink strength is increased as well. This is consistent with earlier conclusions by Cock et al. (1979). The sink strength might be increased through an increase in the number of storage roots, but also through greater secondary growth or longer storage roots. We found that maximum storage root mass and photosynthesis rates at 84 DAP were achieved through a combination of traits that aim at increasing both source and sink strength (Fig. 8). It is often thought that shoot growth in cassava can go at the cost of storage root formation (Lenis et al. 2006). For example, Barros et al. (1978) found that denser plantings of cassava increased the LAI, but decreased storage root mass. In our young plants, we did not find this trade-off, rather more leaves did not decrease storage root yield and increased overall photosynthesis. This is because the canopy had not fully closed and the optimal LAI (2–4; Cock et al. 1979; Mahakosee et al. 2022; Phoncharoen et al. 2022) had not been reached (LA of 0.6 m2 corresponds with an LAI of 1.7, Fig. 8). We conclude that an effort to increase source strength through improved photosynthetic rates in cassava could be unsuccessful without sufficient sink capacity. Increasing the number of storage roots in combination with faster development of the canopy might enhance cassava root yield.

We presented a crop growth model of cassava with its ability to simulate the corresponding 3D root system structure. The model, however, could be further improved: (1) parameterization for leaf and root development might be improved using more data to resolve the apparent deviations in mass fractions (Alves 2001). Secondary root growth was a very important factor in the estimated masses and carbon balance, but little data is currently available for this parameterization. (2) Simulation of the effects of environmental factors on plant growth and development. Environmental factors, such as the availability of nitrogen and phosphorus, and C/N ratio have been reported to be determinant factors for root traits, carbon partitioning, tuber formation, and yield (Cruz et al. 2003; Phuntupan and Banterng 2017; Zheng et al. 2018).The MeOSR model includes a hydrology and nutrient module that simulates the movement of water through the soil and plant and into the atmosphere. It is able to calculate water and nutrient acquisition based on root system architecture and take into account the effects on plant growth. However, these modules need parameterization and validation which were not possible with the available data. (3) The data availability only permitted parameterization of the first 3 months of growth. Extension of the simulated period to cover storage root bulking (~ 6–8 MAP) is necessary to draw final conclusions on yield and how it is influenced by the root phenotype.

Conclusions

Our simulation results provide insights into the dynamics of carbon partitioning, starting from the initial planting till the early bulking of storage roots. The simulation results agreed well with most of the measured plant traits. The model provided insights into the dynamics of carbon allocation. Growth was sink-limited most of the time and, as a consequence, NSC accumulated. This was especially so prior to storage root formation and is consistent with the hypothesis that the accumulation of NSC induces storage root. Storage root formation greatly increases sink strength and leads to the reallocation of NSC to the storage roots in the form of starch accumulation. Increasing sink strength can increase growth, especially if both the leaf area expansion rate and the number of storage roots are increased. This basically means that cassava could have greater early vigor leading to a faster crop establishment. Given that cassava takes three months till canopy closure, and that this is slow compared to many other crops, we think the model might be accurate. Greater vigor might lead to greater water and nutrient use, which needs to be studied.